Definição intervalar da função densidade de probabilidade com distribuição beta: aritmética de moore e aritmética multidimensional RDM

Abstract

When working with numerical calculations in computational environments, we operate on floating point numbers. Thus, the result is only an approximation of a real value and errors created by rounding or truncation can be lead to incorrect results, which cannot be considered as accurates without an error analysis. When using ranges to represent real values, it becomes possible to control the spread of these errors, since interval results have quality assurance. To obtain the numerical value of density functions of continuous random variables with distributions is required the use of numerical integration. If the result is obtained by approximation, it is affected by errors. In this context, this work has the objective of define the probability density function with Beta distribution using the interval extension method, by following some criteria of choose, and subsequently, to implements this functions using programming language with support to interval type. Two approaches to interval arithmetic will be considered: The interval arithmetic of Moore and the multidimensional RDM interval-arithmetic. In order to verify the quality of the interval results obtained, an error analysis will be done by calculating the relative error, absolute error and interval diameter metrics. Then, in order to complement the work, a complexity analysis of the developed algorithms will be done. The goal is to verify that, when using interval arithmetic to calculate probability density function of continuous random variables with distributions, it is possible to has an automatic error control with reliable limits and also, maintain the computation effort for the calculations with real entries.